TY - JOUR

T1 - Parameterized complexity of the list coloring reconfiguration problem with graph parameters

AU - Hatanaka, Tatsuhiko

AU - Ito, Takehiro

AU - Zhou, Xiao

N1 - Funding Information:
We would like to express our gratitude to all anonymous referees of the preliminary version and this journal version for their helpful comments and suggestions. We also thank Yota Otachi for fruitful discussions with him. This work is partially supported by JST CREST Grant Number JPMJCR1402, and by JSPS KAKENHI Grant Numbers JP16J02175, JP16K00003, and JP16K00004, Japan.
Funding Information:
We would like to express our gratitude to all anonymous referees of the preliminary version and this journal version for their helpful comments and suggestions. We also thank Yota Otachi for fruitful discussions with him. This work is partially supported by JST CREST Grant Number JPMJCR1402 , and by JSPS KAKENHI Grant Numbers JP16J02175 , JP16K00003 , and JP16K00004 , Japan.
Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2018/8/29

Y1 - 2018/8/29

N2 - Let G be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. For two given list colorings of G, we study the problem of transforming one into the other by changing only one vertex color assignment at a time, while at all times maintaining a list coloring. This problem is known to be PSPACE-complete even for bounded bandwidth graphs and a fixed constant k. In this paper, we study the fixed-parameter tractability of the problem when parameterized by several graph parameters. We first give a fixed-parameter algorithm for the problem when parameterized by k and the modular-width of an input graph. We next give a fixed-parameter algorithm for the shortest variant which computes the length of a shortest transformation when parameterized by k and the size of a minimum vertex cover of an input graph. As corollaries of these two results, we show that the problem for cographs and the shortest variant for split graphs are fixed-parameter tractable even when only k is taken as a parameter. On the other hand, we prove that the problem is W[1]-hard when parameterized only by the size of a minimum vertex cover of an input graph.

AB - Let G be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. For two given list colorings of G, we study the problem of transforming one into the other by changing only one vertex color assignment at a time, while at all times maintaining a list coloring. This problem is known to be PSPACE-complete even for bounded bandwidth graphs and a fixed constant k. In this paper, we study the fixed-parameter tractability of the problem when parameterized by several graph parameters. We first give a fixed-parameter algorithm for the problem when parameterized by k and the modular-width of an input graph. We next give a fixed-parameter algorithm for the shortest variant which computes the length of a shortest transformation when parameterized by k and the size of a minimum vertex cover of an input graph. As corollaries of these two results, we show that the problem for cographs and the shortest variant for split graphs are fixed-parameter tractable even when only k is taken as a parameter. On the other hand, we prove that the problem is W[1]-hard when parameterized only by the size of a minimum vertex cover of an input graph.

KW - Combinatorial reconfiguration

KW - Fixed-parameter algorithm

KW - Graph algorithm

KW - List coloring

KW - W[1]-hardness

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U2 - 10.1016/j.tcs.2018.05.005

DO - 10.1016/j.tcs.2018.05.005

M3 - Article

AN - SCOPUS:85046738629

VL - 739

SP - 65

EP - 79

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -